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sin ­120o = cos2π = tan3π/2 = ...Study your Unit Circle
for
Quiz #2 Today!
11­3 Answers:
1.
3.
5.
7.
9. Sin π/4 =
10. Sin ­π/4 =
Cos π/4 =
Cos ­π/4 =
Tan π/4 =
Tan ­π/4 =
11. Sin ­5π/4 =
Cos ­5π/4 =
12. Sin ­5π/6 =
Cos ­5π/6 =
Tan ­5π/4 =
Tan ­5π/6 =
13. Sin 11π/6=
14. Sin 2π/3=
Cos 11π/6=
Cos 2π/3=
Tan 11π/6=
Tan 2π/3=
15. Sin 4π/3=
16. Sin 7π/4 =
Cos 4π/3=
Cos 7π/4 =
Tan 4π/3=
Tan 7π/4 =
Notes 11­4: The SIX Trigonometric Functions
You already know the following 3 trig functions represent the sides of the special right triangles in the unit circle.
Sine
abbreviated: sin Cosine abbreviated: cos and Tangent abbreviated: tan 60
45
You already know the INVERSE for each is
30
What you may not realize is each of these is the reciprocal of:
abbreviated: sin­1 =
Sine
abbreviated: cos­1 =
and abbreviated: tan­1 =
Cosine
and Tangent
Now meet:
Secant
abbreviated: sec = cos­1 ­1
sin
Cosecant abbreviated: csc =
and ­1
tan
Cotangent abbreviated: cot =
These 3 trig. functions ALSO represent the reciprocal of the one of the first 3 Trig functions...
­1
a.k.a. ( sin
, , ) can you guess which? :)
cos­1 tan­1
SIX Trigonometric Functions
The reciprocal
of ... Sine
= Cosecant
Cosine
and Tangent
= Secant
and = Cotangent
How does this affect the coordinates of our circle?
Lets look at a chart!
Find the Secant of each of the following angles.
o
60
90o
0 30 45
0 π/6 π/ 4 π / 3 π / 2
o
o
o
θ:
Cosθ
Secθ
Cosθ
"RECIPROCALS"
Hint: (Cos­1) = (Sec) (Cos, Sin) Cosines and Secants
Find the Cosecant of each of the following angles.
o
o
o
0 30 45 60 90o
π
π
π
π
0 /6 /4 /3 /2
o
θ:
Sinθ
Cscθ
Sinθ "RECIPROCALS"
­1
Hint: (Sin ) = (Csc) (Cos, Sin) Sines and Cosecants.
Find the Cotangent of each of the following angles.
0
θ:
o
o
o
o
30 45 60 90
o
Tanθ=
sin/cos
Cotθ=
cos/sin
Tanθ "RECIPROCALS"
­1
Hint: (Tan ) = (Cot) (Cos, Sin) Tangents and Cotangents
Ignore the Denominators!
Hint #1: (Cos, Sin) and Tan = Sin/Cos
Alpha­Order
Hint #2: (Sec, Csc) and Cot = Cos/Sin
Reciprocals = Reverse Alpha­Order
Note: For COtangent the COsine is on top!
Assignment 11­4
Page 345
#2­8 even, 17­22 all
Only 10 problems!!!
Please remember to show all your work!